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Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) dimensional analogs of three-dimensional objects, e.g. hypercube, hyperplane, hypersphere. n-dimensional polyhedra are called polytopes. The four-dimensional cases of general n-dimensional objects are often given special names, such as those summarized in the following table.

The 120-cell is a finite regular four-dimensional polytope with Schläfli symbol . It is also known as the hyperdodecahedron or hecatonicosachoron, and is composed of 120 dodecahedra, with 3 to an edge. The 120-cell has 600 vertices (Coxeter 1969), and consists of 120 dodecahedra and 720 pentagons (Coxeter 1973, p. 264). The dual of the 120-cell is the 600-cell.

-- HiazHhzz - 16 Nov 2004

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